What techniques have been used to repeat geometry or other detail to the infinite horizon?
To give the impression of infinity, often it's not necessary to copy the object many times at all. you will notice that in the example image only about 8 or 9 repetitions are visible, the implied continuation of cubes is hidden behind a white glare.

One way is to do this is by using an array modifier. One issue with this is that it is not the most efficient, as the array modifier creates new geometry every time the source is repeated. To use the array modifier to make instances (references to a single copy of the mesh data, rather than actually copying the mesh data), e.g. using Dupli objects:


Add a plane (ShiftA> Add > Mesh > Plane) and add an array modifier to it.
Parent the object you want to repeat to plane (select the object, then the plane, and press CtrlP>Object)
Enable Duplifaces on the plane under Properties > Object > Duplication.




Using this technique, you can duplicate fairly high-poly objects many times. In this example I duplicated a 4500 vert cube thing 100 times without any trouble. When I tried this with a straight array modifier (without the dupliface trick) the viewport was quite slow and the array modifier took about 30 seconds to compute.



Cycles is actually pretty good at rendering large amounts of instances like this.

Some examples:


Fun with Instancing in Cycles
19 Billion Polygons, not a ridiculous number anymore (BA thread)




Note that depending on the scene, there might be other optimizations you can do, e.g. using baked texture maps and lower poly models for far away objects.